Lyapunov Functions and Stability of Caputo Fractional Differential Equations with Delays

被引：18

作者：

Agarwal, Ravi ^{[1
,2
]}

Hristova, Snezhana ^{[3
]}

O'Regan, Donal ^{[4
]}

机构：

[1] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX 78363 USA

[2] Florida Inst Technol, 150 West Univ Blvd, Melbourne, FL 32901 USA

[3] Univ Plovdiv Paisii Hilendarski, Dept Appl Math & Modeling, Plovdiv, Bulgaria

[4] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

来源：

DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2022年 / 30卷 / 03期

关键词：

Caputo fractional differential equations; Lyapunov functions; Stability; Fractional derivative of Lyapunov functions; SYSTEMS; THEOREM; TIME;

D O I：

10.1007/s12591-018-0434-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The direct Lyapunov method is extended to nonlinear Caputo fractional differential equations with variable bounded delays. A brief overview of the literature on derivatives of Lyapunov functions is given and applications to fractional equations are discussed. Advantages and disadvantages are illustrated with examples. Sufficient conditions using three derivatives of Lyapunov functions are given and our results are compared with results in the literature. Also fractional order extensions of comparison principle are established.

引用

页码：513 / 534

页数：22

共 29 条

[1] Practical stability with respect to initial time difference for Caputo fractional differential equations [J].